To think that string vibration does not effect your arm is a serious thing to overlook. When we're talking about strings vibrating at extremely high frequencies as they do, it can really irritate things in your elbow as well as your wrist. The effects are perceived differently by each person, but regardless of what you feel, there is a difference in what is transmitted to your arm. What do you think dampens the string vibration without a dampener? It is transmitted directly to the frame and in turn is transmitted to your hand and throughout the rest of your arm.

Frame vibration is another big issue, that depends on the frame and other things. Prince rackets do a great shop of getting rid of this vibration. This is the idea behind Babolats Cortex technology.

Like the others said, softer strings and a standard length rackets are also obvious things to do. If you don't have TE at the moment and are careful and pay attention to any warning sings, you will probably be fine. Keep tensions low on poly's, use a dampener, and use an overgrip to dampen even more shock.